The number of members of an online community increases each month. The function M(t) = N(1 + r)^t represents the number of members at month t, where N is the initial number of members and r is the rate of increase. Select the correct statement.


A. The value of M is a product of N and a factor that does not depend on N.

B. N increases each month.

C. The function is linear.

D. The initial value is (1 + r).

[tex]6.75 \div 3 = 2.25[/tex]

A.$2.25

You take the total which is $6.75 and divide it by the number of dog treat bags she purchased and once you divide it you get the total of one bag which is $2.25 per bag.

I only know the answer for number 4 and 5

4. You subtract the min from the max to find the range.

5. The number that occurs most often in a day's set is called the mode.

Answer:

The answers below are in order going from top to bottum, left to right.

Step-by-step explanation:

mean, dividing, median, average, range, mode

Answer:

The ratio is equal to [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Let

x----> the amount spent on advertising

y----> the amount spent on its website

The ratio is equal to x/y

Remember that

[tex]0.75=\frac{3}{4}[/tex]

so

[tex]\frac{1}{(3/4)}=\frac{4}{3}[/tex]

Answer:

the solution is (-3, -2)

Step-by-step explanation:

Please, separate your equations with a (;) or a (.).  Better yet, write only one equation per line:

y=2x+4

3x−6y=3

Substitute 2x + 4 for y in the second equation:

3x - 6(2x + 4) = 3, or

3x - 12x - 24 = 3

Combining like terms, we get -9x = 27, and so x = -27/9, or x = -3.

Since we know that y=2x+4, we replace x in this equation with -3 and calculate y:

y = 2(-3) + 4 = -2

Then the solution is (-3, -2).

Answer:

34,623

Step-by-step explanation:

427,113 + 38,264 = 465377

500,000 - 465377 = 34,623 books in December must go out to meet the librarian's goal.

3. replace x with 4 and solve:

3(4) - 5 = 12 -5 = 7

The answer is 7

4. Replace x with 6 in the equation for g(x) first:

2(6) -5 = 12-5 = 7

Now replace x with 7 in the equation for f(x)

2(7) +1 = 14 +1 = 15

The answer is 15

Answer:

The average rate of change for this quadratic function is -2.

Step-by-step explanation:

In this question, we have f(x) = y = x^{2} + 4x + 5.

Given a function y, the average rate of change S of y=f(x) in an interval  [x_s, x_f] will be given by the following equation:

S = \frac{f(x_{f}) - f(x_s)}{x_f - x_s}

So, in  your problem, f(x) = x^{2} + 4x + 5, x_{f} = -2 and x_{s} = -4.

Applying these informations to the equation S above, we have:

S = \frac{f(-2) - f(-4)}{-2-(-4)}

Where

f(-2) = (-2)^{2} + 4(-2) +5 = 4-8+5 = 9-8 = 1

f(-4) = (-4)^{2} + 4(-4) +5 = 16-16+5 = 5

So, the average rate of change S will be

S = \frac{1-5}{2} = -4

The expected gain or loss for this store is a gain of $79,750.

Gain is defined as the profit occurred by a store or a shopkeeper when an item is sold at a higher price than it was originally bought.

Loss is defined as the money lost by a store or a shopkeeper when an item is sold at a lower price than it was originally bought.

Both gain or loss is calculated by the formula -

Cost Price (CP) - Selling price (SP)

It is given that the company estimates that there is an 80% chance the store will have a profit of $100,000, a 10% chance of the store will break even, and a 10% chance of the store will lose $2,500.

Calculating the net gain or loss or the company -

= (80% * $100,000) + (10% * $0) - (10% * $2,500)

= (80/100 * $100,000) - (10/100 * $2,500)

= $80,000 - $250

= $79,750

Thus the net gain involved in the business by the company is $79,750 .

Therefore, the expected gain or loss for this store is a gain of $79,750.

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Answer:

It will take Eva 4 hours to catch up with Seth on the trail.

Step-by-step explanation:

1. Seth: 4/hour Eva: 6/hour

2. Hour 1: S:12 E:6

Hour 2: S:16 E:12

Hour 3: S:20 E:18

Hour 4: S:24 E:24

___

Hope this helps you! :)

Answer:

It will take Eva 4 hours to catch up with Seth on the trail.

Answer:

x≥38 points

Step-by-step explanation:

Julio wants to break his school’s scoring record of 864 points during his 24-game basketball season. During the first 8 games of the season, he scored a total of 256 points. Which inequality can be used to find x, the number of points Julio must average per game during the rest of the season to break the record?

julio has a 24 game basketball season.

he has played 8, it means there are 16 more games to go

therefore=

he has scored 256 nts, wic means there are still 608 points to go .

864-256=608

x is the points he more score per every game.

16x=608

to break the records ,he must score an extra point 1

so 16x≥608

x≥38

Answer:

256 + 16x > 864

Answer:

a model is an estimate or approximation of a data set. In the real world, there are too many variables to know exactly what will happen. However, if a model is a good fit, then it can be used to make predictions about what will happen. With a useful model, a predicted value should be a good estimate of an observed value.

Step-by-step explanation:

Took the assignment

George Box's statement "All models are wrong, but some are useful" suggests that while models are imperfect, they still offer valuable insights and utility in understanding complex systems.

George Box's statement "All models are wrong, but some are useful" acknowledges the inherent imperfections of models, emphasizing that they are simplified representations of reality.

Models, by nature, cannot perfectly capture every detail of a complex system.

However, despite their inaccuracies, models still hold utility in providing insights and aiding decision-making processes.

This perspective suggests that while models may not be entirely accurate, they can still offer valuable understanding and predictive power.

Box's statement encourages a balanced approach, where users recognize the limitations of models while leveraging their practical usefulness.

In essence, it underscores the importance of not dismissing models due to their imperfections but rather using them judiciously in specific contexts where they can provide meaningful insights.

Answer:

A. 2 to 5

Step-by-step explanation:

x is being multiplied by 2.

y is being multiplied by 5.

Although there is an infinite amount of ratios we can use when we know the values,we don't have that right now, so we have to stick to 2 to 5, which is our answer.

Answer:

Good ways to sample

Simple random sample: Every member and set of members has an equal chance of being included in the sample. Technology, random number generators, or some other sort of chance process is needed to get a simple random sample.

Example—A teachers puts students' names in a hat and chooses without looking to get a sample of students.

Why it's good: Random samples are usually fairly representative since they don't favor certain members.

Stratified random sample: The population is first split into groups. The overall sample consists of some members from every group. The members from each group are chosen randomly.

Example—A student council surveys 100 students by getting random samples of 25 freshmen, 25 sophomores, 25 juniors, and 25 seniors.

Why it's good: A stratified sample guarantees that members from each group will be represented in the sample, so this sampling method is good when we want some members from every group.

Cluster random sample: The population is first split into groups. The overall sample consists of every member from some of the groups. The groups are selected at random.

Example—An airline company wants to survey its customers one day, so they randomly select 555 flights that day and survey every passenger on those flights.

Why it's good: A cluster sample gets every member from some of the groups, so it's good when each group reflects the population as a whole.

Example—A principal takes an alphabetized list of student names and picks a random starting point. Every 20th student is selected to take a survey.

Bad ways to sample

Convenience sample: The researcher chooses a sample that is readily available in some non-random way.

Example—A researcher polls people as they walk by on the street.

Why it's probably biased: The location and time of day and other factors may produce a biased sample of people.

Voluntary response sample: The researcher puts out a request for members of a population to join the sample, and people decide whether or not to be in the sample.

Example—A TV show host asks his viewers to visit his website and respond to an online poll.

Step-by-step explanation:

In a statistical study, sampling methods refer to how we select members from the population to be in the study.

If a sample isn't randomly selected, it will probably be biased in some way and the data may not be representative of the population.

There are many ways to select a sample—some good and some bad.

It should be $879.34, already rounded.

Answer:

a, Addition is commutative, so n+23.4023.40+n equals 1.

Step-by-step explanation:

Let [tex]x[/tex] be the amount (gal) of the 40% slime solution you end up using. You want to end up with 120 gal of the 50% solution, so that you would use [tex]120-x[/tex] gal of the 70% solution.

You want the final solution to consist of 50% slime, or 60 gal of slime. Each gal of the 40% solution contributes 0.4 gal of slime, while each gal of the 70% solution contributes 0.7 gal of slime. This means

[tex]0.4x+0.7(120-x)=0.5\cdot120=60[/tex]

[tex]\implies0.4x+84-0.7x=60[/tex]

[tex]\implies24=0.3x[/tex]

[tex]\implies x=80[/tex]

so the answer is B.

Answer:

[tex]\large\boxed{x=11}[/tex]

Step-by-step explanation:

Use Angel Bisector Theorem (look at the picture),

[tex]\dfrac{3x-3}{24}=\dfrac{5x}{44}\qquad\text{cross multiply}\\\\44(3x-3)=24(5x)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(44)(3x)+(44)(-3)=120x\\\\132x-132=120x\qquad\text{add 132 to both sides}\\\\132x=120x+132\qquad\text{subtract}\ 120x\ \text{from both sides}\\\\12x=132\qquad\text{divide both sides by 12}\\\\x=11[/tex]

Answer:

1) The height the ball will bounce after hitting the ground the fourth time = 2.0736ft

2) The building is strong enough to withstand the Denali earthquake

Step-by-step explanation:

1) According to the given statement Bradley dropped the ball from a roof 16 feet high.Each time the ball hits the ground, it bounces3/5 the previous height

Therefore,

First bounce = 16*3/5 = 9.6

Second bounce = 9.6 *3/5 = 5.76

Third bounce =  5.76*3/5=3.456

Fourth bounce = 3.456*3/5=2.0736

The height the ball will bounce after hitting the ground the fourth time = 2.0736ft....

2) The 2002 Denali earthquake in Alaska had a Richter scale magnitude of 6.7.

Denali earthquake = 6.7 * 70 =469

It means that the building in Denali should be strong enough to withstand an earthquake of that magnitude  

The 2003 Rat Islands earthquake in Alaska had a Richter scale magnitude of 7.8

Rat Islands earthquake = 7.8 * 30 = 234

It means that the building in Rat Islands should be strong enough to withstand an earthquake of that magnitude....

Answer:

Part 1) The volume of the composite figure is [tex]620.7\pi\cm^{3}[/tex]

Part 2) The surface area of the composite figure is [tex]273\pi\ cm^{2}[/tex]

[tex]V=620.7\pi\cm^{3}, S=273\pi\ cm^{2}[/tex]

Step-by-step explanation:

Part 1) Find the volume of the composite figure

we know that

The volume of the figure is equal to the volume of a cone plus the volume of a hemisphere

Find the volume of the cone

The volume of the cone is equal to

[tex]V=\frac{1}{3} \pi r^{2} h[/tex]

we have

[tex]r=7\ cm[/tex]

Applying Pythagoras Theorem find the value of h

[tex]h^{2}=25^{2} -7^{2} \\ \\h^{2}= 576\\ \\h=24\ cm[/tex]

substitute

[tex]V=\frac{1}{3} \pi (7)^{2} (24)[/tex]

[tex]V=392 \pi\cm^{3}[/tex]

Find the volume of the hemisphere

The volume of the hemisphere is equal to

[tex]V=\frac{4}{6}\pi r^{3}[/tex]

we have

[tex]r=7\ cm[/tex]

substitute

[tex]V=\frac{4}{6}\pi (7)^{3}[/tex]

[tex]V=228.7\pi\cm^{3}[/tex]

therefore

The volume of the composite figure is equal to

[tex]392 \pi\cm^{3}+228.7\pi\cm^{3}=620.7\pi\cm^{3}[/tex]

Part 2) Find the surface area of the composite figure

we know that

The surface area of the composite figure is equal to the lateral area of the cone plus the surface area of the hemisphere

Find the lateral area of the cone

The lateral area of the cone is equal to

[tex]LA=\pi rl[/tex]

we have

[tex]r=7\ cm[/tex]

[tex]l=25\ cm[/tex]

substitute

[tex]LA=\pi(7)(25)[/tex]

[tex]LA=175\pi\ cm^{2}[/tex]

Find the surface area of the hemisphere

The surface area of the hemisphere is equal to

[tex]SA=2\pi r^{2}[/tex]

we have

[tex]r=7\ cm[/tex]

substitute

[tex]SA=2\pi (7)^{2}[/tex]

[tex]SA=98\pi\ cm^{2}[/tex]

Find the surface area of the composite figure

[tex]175\pi\ cm^{2}+98\pi\ cm^{2}=273\pi\ cm^{2}[/tex]

For this case we have by definition, that the total surface area of a regular pyramid with a square base is given by:

[tex]SA = \frac {1} {2} p * S + A_ {b}[/tex]

Where:

p: It is the perimeter of the base

S: It's the inclination

[tex]A_ {b}:[/tex] It is the area of the base

Substituting:

[tex]A_ {b} = 7 ^ 2 = 49units ^ 2\\p = 7 + 7 + 7 + 7 = 28units\\S = 10units\\SA = \frac {1} {2} 28 * 10 + 49\\SA = 140 + 49\\SA = 189 \ units ^ 2[/tex]

ANswer:

Option B

Answer:

B. 189 units squared

Step-by-step explanation:

ap3x

Assume a general solution of the form

[tex]y(x)=\displaystyle\sum_{n\ge0}a_nx^n[/tex]

with derivatives

[tex]y'(x)=\displaystyle\sum_{n\ge0}na_nx^{n-1}=\sum_{n\ge1}na_nx^{n-1}[/tex]

[tex]y''(x)=\displaystyle\sum_{n\ge0}n(n-1)a_nx^{n-2}=\sum_{n\ge2}n(n-1)a_nx^{n-2}[/tex]

Substituting into the ODE gives

[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-2\sum_{n\ge1}na_nx^n+4\sum_{n\ge0}a_nx^n=0[/tex]

The first sum starts with degree 0; the second starts with degree 1; and the third starts with degree 0. So remove the first term from the first and third sums, then consolidate everything into one sum by shifting indices as needed.

First sum:

[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}=2a_2+\sum_{n\ge3}n(n-1)a_nx^{n-2}[/tex]

[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}=2a_2+\sum_{n\ge1}(n+2)(n+1)a_{n+2}x^n[/tex]

Third sum:

[tex]\displaystyle\sum_{n\ge0}a_nx^n=a_0+\sum_{n\ge1}a_nx^n[/tex]

So the ODE can be expressed as

[tex]\displaystyle\left(2a_2+\sum_{n\ge1}(n+2)(n+1)a_{n+2}x^n\right)-2\sum_{n\ge1}na_nx^n+4\left(a_0+\sum_{n\ge1}a_nx^n\right)=0[/tex]

[tex]\displaystyle2a_2+4a_0+\sum_{n\ge1}\bigg((n+2)(n+1)a_{n+2}+(4-2n)a_n\bigg)x^n=0[/tex]

Then the coefficients are given by the recurrence,

[tex]\begin{cases}a_0=a_0\\a_1=a_1\\2(2-n)a_n+(n+2)(n+1)a_{n+2}=0&\text{for }n\ge0\end{cases}[/tex]

Notice that we should have [tex]a_0\neq0[/tex] and [tex]a_1\neq0[/tex] in order to get non-zero solutions.

For [tex]n=2[/tex], we would find that [tex]a_4=0[/tex], which would imply that [tex]a_n=0[/tex] for all even [tex]n\ge2[/tex]. Then the even-indexed terms in the series contribute one solution,

[tex]y_1(x)=a_0+a_2x^2=a_0(1-2x^2)[/tex].

On the other hand, for odd [tex]n\ge1[/tex] we have

[tex]a_{n+2}=\dfrac{2(n-2)}{(n+2)(n+1)}a_n[/tex]

With [tex]n=1[/tex]:

[tex]a_3=\dfrac{2\cdot(-1)}{3\cdot2}a_1=-\dfrac2{3!}a_1[/tex]

With [tex]n=3[/tex]:

[tex]a_5=\dfrac{2\cdot1}{5\cdot4}a_3=-\dfrac{2^2\cdot1}{5!}a_1[/tex]

With [tex]n=5[/tex]:

[tex]a_7=\dfrac{2\cdot3}{7\cdot6}a_5=-\dfrac{2^3\cdot3\cdot1}{7!}a_1[/tex]

So the general pattern for [tex]n=2k+1[/tex], [tex]k\ge1[/tex], is

[tex]a_{2k+1}=-\dfrac{2^k\prod\limits_{i=1}^{k-1}(2i-1)}{(2k+1)!}a_1[/tex]

and we get a second (linearly independent) solution

[tex]y_2(x)=a_1x+\displaystyle\sum_{k\ge1}a_{2k+1}x^{2k+1}[/tex]

The recursive function describes the number of bacteria observed at the nth hour is; aₙ = 5 * (4)ⁿ ⁻ ¹

We are given the geometric sequence as; 5, 20, 80, 320, 1,280

We know that the general formula to find the nth term of a geometric sequence is; aₙ = arⁿ ⁻ ¹

Where;

a is first term

r is common ratio

Thus, the recursive function is;

aₙ = 5 * (4)ⁿ ⁻ ¹

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The recursive function for the number of bacteria observed at the nth hour is B(n) = 4 × B(n-1), where B(1) is 5 and n > 1, indicating that the number of bacteria quadruples every hour.

To describe the number of bacteria observed at the nth hour, we need to devise a recursive function based on the given sequence: 5, 20, 80, 320, 1280. Analyzing the sequence, we see that each term is four times the previous term. Therefore, the recursive function that describes this sequence is:

B(n) = 4 × B(n-1), where B(1) = 5 and n > 1.

This recursive function states that to obtain the number of bacteria at any hour n, you multiply the number of bacteria from the previous hour by 4. For example, to find the number of bacteria at hour 3 (third term), you would calculate 4 times the number of bacteria at hour 2, which is 4 × 20 = 80, matching the given sequence.

Answer:

-2

Step-by-step explanation:

It's when the graph crosses the y axis

Find the Y value when the graphed line is at X = 0

When X is 0, the line crosses The X- axis at Y = -2

Answer:

[tex]\large\boxed{4\vec{u}+3\vec{v}=<-26,\ 26>}[/tex]

Step-by-step explanation:

[tex]\vec{u}=<-5,\ 2>;\ \vec{v}=<-2,\ 6>\\\\4\vec{u}=<(4)(-5),\ (4)(2)>=<-20,\ 8>\\\\3\vec{v}=<(3)(-2),\ (3)(6)>=<-6,\ 18>\\\\4\vec{u}+3\vec{v}=<-20,\ 8>+<-6,\ 18>=<-20+(-6),\ 8+18>=<-26,\ 26>[/tex]

The result of the vector addition and scalar multiplication operation 4u + 3v, with u=<-5,2> and v=<-2,6>, is <-26,26>.

Given the vectors u=<-5,2> and v=<-2,6>, we can compute the expression 4u + 3v by performing vector addition and scalar multiplication.

First, we multiply the vectors by their respective scalars, which results in 4u = 4*(-5,2) = <-20,8> and 3v = 3*(-2,6) = <-6,18>.

Then we add the resulting vectors together. The x-components add together to produce the new x-component and the y-components add together to produce the new y-component. So 4u + 3v = <-20,8> + <-6,18> = <-26,26>.

This demonstrates the distributive property and the principles of vector addition and scalar multiplication.

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P(5,2) =  n! /(n-r)!

n = 5, r = 2:

= (5 x 4 x 3 x 2 x 1 ) /  3 x 2 x 1

Cancel out common factors:

= 5 x 4 = 20

The answer is 20.

Answer:

P (5,2) = 20

Step-by-step explanation:

First of all, we must understand two basic concepts:

A permutation is the variation of the order or position of the elements of an ordered set or a tuple.

The factorial function (symbol:!) Means that descending numbers are multiplied.

The formula to solve the permutation is:

[tex]\frac{n!}{(n-r)!}[/tex]

where "n" is the number of things you can choose, and you choose "r" from them (it cannot be repeated, order matters).

In the given case ...

P (n, r) = [tex]\frac{n!}{(n-r)!}[/tex]

Being n = 5, and r = 2

[tex]P(5,2)=\frac{5!}{(5-2)!}=\frac{5!}{3!}=\frac{5*4*3!}{3!}=5*4=20[/tex]

P (5,2) = 20

-------------------------------------------------- ----------------------------

I hope this helps!

Answer:

surface area of a sphere= 4pi*r^2

S.A when radius is 7 is:

=4pi*(7)^2

=196pi cm^2

if you multiply radius by 4, the equation becomes:

4pi*(4r)^2

=4pi*16r^2

=64pi*r^2

substitute 7 into equation:

=64pi*(7)^2

=64pi*49

=3136pi cm^2

Divide new S.A. by old S.A. to show effect:

=3136pi/196pi

=16

If the radius is multiplied by 4, the effect on the surface area is that it is 16 times the surface area of the sphere where the radius is not multiplied.

If the radius of a sphere of radius 7 cm is multiplied by 4, then its surface area is increased 16 times than the initial surface area.

Suppose that radius of the considered sphere is of 'r' units.

Then, its surface area S would be:

[tex]S = 4\pi r^2 \: \rm unit^2[/tex]

For this case, we're specified that:

We've to find the effect on the surface area of the sphere.

Initial surface area:

[tex]S_i = 4\pi r^2 = 4 \pi (7)^2 \: \rm unit^2[/tex]
Final surface area:

[tex]S_f = 4\pi r^2 = 4 \pi (4 \times 7)^2 = 4^2 \times [4 \pi (7)^2] \: \rm unit^2\\\\S_f =16 \times S_i[/tex]

Thus, if the radius of a sphere of radius 7 cm is multiplied by 4, then its surface area is increased 16 times than the initial surface area.

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Can you tell me what do you mean exactly by menu of 8, so i can help you.

Answer:

Step-by-step explanation:

Let s represent the length of the shorter part (in feet). Then the longer part has length (s+1), and the total length of the two parts is ...

  s + (s+1) = 25

  2s = 24 . . . . . . . subtract 1, simplify

  s = 12 . . . . . . . . . divide by 2; the length of the shorter part

  s+1 = 13 . . . . . . . the length of the longer part

The shorter part is 12 feet long; the longer part is 13 feet long.

_____

Comment on this problem type

You will note that the smaller number is half the difference of the total length (25) and the difference in lengths (1). This is the generic solution to a "sum and difference" problem. The smaller number is half the difference of the given numbers, and the larger number is half their sum: (25+1)/2 = 13.

Answer:

8 and 17

Step-by-step explanation:

Let's say the smaller number is x. The question says "The longer part is one foot more than twice the shorter part" so we reverse that using x which becomes x+2x+1=25 and x=8 so 8+8*2+1=25 => 8+17=25 so the answer is 8 and 17, please like and 5 star rate

ANSWER

-2,-1,0,+4,+6

EXPLANATION

The given integers are:

-1, +6, 0, +4, -2

To arrange from least to greatest means arranging in ascending order of magnitude.

We can observe that:

-2<-1<0<+4<+6

Therefore the numbers written in order from least to greatest is:

-2,-1,0,+4,+6

Answer: 144°

Step-by-step explanation:

It is a regular pentagon which means all five sides are the same length. This also means that the angle between any two adjacent vertices is the same. So to find the angle between two adjacent vertices we take 360° and divide it by 5 which equals 72°. But A and D are not adjacent to each other, they have E in the middle (it also has B and C in the middle on the other side, but that's the bigger angle, and we usually label angles through their smaller angle. ex: a 30° angle is 30° if you look at it on the smaller angle (∠ ← here), but if you look at the bigger side of the angle (here →∠) it is 330°, yet we still call it a 30° angle). So, between A and D are two equal angles A to E, and E to D. So we multiply 72° by 2 which equals 144°.

So the answer is 144°.

Answer:

144

Step-by-step explanation:

plato